Direct and inverse Hall effects: A consequence of both Ampere's law and electron spin?

DIPC Seminars

Antonio Hernando, Universidad Complutense Madrid, Spain
Donostia International Physics Center
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Direct and inverse Hall effects: A consequence of both  Ampere's  law and electron spin? We analyse the contribution of the inhomogeneous magnetic field induced by an electrical current to the spin Hall effect in metals. In fact the field produced by the current cannot act on the current itself but the field produced by the relative motion of the lattice does it. The Zeeman coupling between the field, seen at the reference frame in which the carriers are at rest, and the electron spin leads to a force that accumulates spin at the edges. It is shown that this spin Hall effect can be expressed as two opposite ordinary Hall effect in which the applied fields are the saturation magnetization of both sub-bands. In other words the force exerted by the lattice current on the electron, ( ±(µ∇)B where B is the field seen by the electrons and µ the spin magnetic moment) is equal but opposite to that exerted by the electrons on the lattice current ( ± jµ_0 M, where M is the saturation magnetiztion of ± spin subbands. ) The inverse spin Hall effect is also explained under the same basis. Finally, by considering the effect of the possible spontaneous magnetization of the lattice, a new perspective for understanding the anomalous Hall effect is open. It is concluded that , the Lorentz force, the Zeeman energy and the spin of the electron are ingredients sufficient to account for the first order characteristics of the spin Hall effect. Within our explanation, that does not interact with other possible contributions, we remark the following characteristics a) The field produced by the lattice current on the carrier system defines a spin direction b) Not explicit dependence of the effect strength on the atomic spin-orbit coupling of the metal is envisaged at first order c) The huge dispersion of experimental results can be understood through the geometrical dependence of the magnetic field strength and distribution d) The effect of the macroscopic field is naturally introduced, otherwise a non realistic assumption as that implict in Hirsch discussion: “ the number of impurities is equal to the number of lattice atoms and all of them are identical” has to be established a priori e) The order of magnitude of both spin and charge imbalances inferred from our considerations is that found in the literature Host: Ricardo Díez Muiño